Spectral densities from Euclidean lattice correlators via the Mellin transform

TL;DR

This paper introduces a method using the Mellin transform to derive explicit formulas for spectral densities from Euclidean lattice correlators, facilitating non-perturbative analysis in quantum field theories.

Contribution

It provides a novel analytic approach employing the Mellin transform to extract spectral densities from lattice correlation functions, applicable in both continuum and lattice settings.

Findings

Derived explicit Mellin transform formulas for spectral densities.

Extended the method to smeared spectral densities.

Applicable to various quantum field theory calculations.

Abstract

Spectral densities connect correlation functions computed in quantum field theory to observables measured in experiments. For strongly-interacting theories, their non-perturbative determinations from lattice simulations are therefore of primary importance. They entail the inverse Laplace transform of correlation functions calculated in Euclidean time. By making use of the Mellin transform, we derive explicit analytic formulae to define spectral densities from the time dependence of correlation functions, both in the continuum and on the lattice. The generalization to smeared spectral densities turns out to be straightforward. The formulae obtained here within the context of lattice field theory can be easily applied or extended to other areas of research.